Max Upward Force to Hold Bowling Ball on Wall

[mattbeatlefreak]

Homework Statement

A 4.5-kg bowling ball is perched on a concrete ledge directly below your dorm room window, with the side of the ball opposite the holes touching the wall. Wanting to hold the ball in place so that it doesn't roll off and land on somebody, you manage to hook one of the holes with a wire and exert a purely tangential (and vertical) force on the ball. The coefficient of static friction between ball and ledge is the same as that between ball and wall, μs = 0.43. What is the maximum upward force you can exert so that the ball does not rotate and you lose your hold? Even though the ball has holes drilled in it, assume a uniform distribution of inertia.

Homework Equations

τ = Fr
F = ma
ƒ = μN

The Attempt at a Solution

I drew a diagram and wrote equations for net torque, net force in x direction, and net force in y direction.

τ_net=T-ƒ_wall-ƒ_ledge=0
F_x=ƒ_ledge-N_wall=0
F_y=T-mg+N_ledge+ƒ_wall=0

To find the maximum force, I set the frictional force from the wall = μ times the normal force from the ledge. Also, I set the frictional force from the ledge = μ times the normal force from the wall.

Substituting values:
T-.43N_ledge-.43N_wall=0
.43N_wall-N_wall=0
T-44.1+N_ledge+.43N_ledge=0

Solving for N_{wall gave a value of 0, which doesn't seem correct. Continuing through regardless, I finished with an answer of 10.2 N for the tension, which wasn't correct.}

 

[haruspex]

I set the frictional force from the wall = μ times the normal force from the ledge. Also, I set the frictional force from the ledge = μ times the normal force from the wall.

Did you really do that? A little unconventional perhaps?

 

[mattbeatlefreak]

Did you really do that? A little unconventional perhaps?

I was told to do that from a tutor I was seeking help from. Clearly there was some misthought or miscommunication.

 

[haruspex]

I was told to do that from a tutor I was seeking help from. Clearly there was some misthought or miscommunication.

What's the usual relationship between maximum frictional force and normal force?

 

[mattbeatlefreak]

What's the usual relationship between maximum frictional force and normal force?

ƒ_s = μ_s x F_N

 

[haruspex]

ƒ_s = μ_s x F_N

Yes, but what are those two forces exactly? Where do they act and in what directions in relation to each other?

 

[mattbeatlefreak]

Yes, but what are those two forces exactly? Where do they act and in what directions in relation to each other?

Since friction is along a surface, and normal force is perpendicular to the surface, the forces should be perpendicular to one another. So in this case, the max friction force (along wall) would equal the μ_s times the normal force from the wall? And same thing for the ledge?

 

[haruspex]

Since friction is along a surface, and normal force is perpendicular to the surface, the forces should be perpendicular to one another. So in this case, the max friction force (along wall) would equal the μ_s times the normal force from the wall? And same thing for the ledge?

Yes.

 

[mattbeatlefreak]

Yes.

I got 15 N for the tension, and this answer is correct. Thanks for all your help!

 

[Scigirl]

Care to explain further? I'm stumped on this one too.

 

[haruspex]

Care to explain further? I'm stumped on this one too.

As with the initial post of a thread, if you have the same homework you need to post your attempt.
Have you drawn a diagram? What forces act on the ball?

 

[Scigirl]

Fx=Normalforce (wall)-Friction (ledge)=0
Fy=Normal(ledge)+Tension-mg-friction(wall)=0

Solved for Y direction for Normal Force Fn= (mg-T)/0.57
Then plugged into T=mg-fs-Fn

 

[haruspex]

Fx=Normalforce (wall)-Friction (ledge)=0
Fy=Normal(ledge)+Tension-mg-friction(wall)=0

You have two equations but three unknowns. What do you need to do?

 

[Scigirl]

You have two equations but three unknowns. What do you need to do?

Do I need a third equation? f=μN?

 

[haruspex]

Do I need a third equation? f=μN?

You need a third equation, but I was assuming you were already using f=μN. (If not, you had five unknowns.)
In 2D statics problems, there are always three equations available. Exactly which three is a matter of choice, but the usual choice is horizontal linear force balance, vertical linear force balance, and ...?

 

[Scigirl]

You need a third equation, but I was assuming you were already using f=μN. (If not, you had five unknowns.)
In 2D statics problems, there are always three equations available. Exactly which three is a matter of choice, but the usual choice is horizontal linear force balance, vertical linear force balance, and ...?

Rotational force? Torque perhaps? Torque=rF

 

[haruspex]

Rotational force? Torque perhaps? Torque=rF

Yes.

 

[Scigirl]

Yes.

I'm not sure how to use torque in this situation, is the Net torque from the tension and the 2 frictions?

 

[haruspex]

I'm not sure how to use torque in this situation, is the Net torque from the tension and the 2 frictions?

All the forces contribute to torque in principle, but you can eliminate some by choosing an axis through which the forces pass. E.g. if you choose the centre of the ball then you can ignore the normal forces because they have no torque about that point.

 

[Scigirl]

Στ=τT-2τf
Tr=2(μFn)r
T=2μ[(mg-T)/(1-μ)]
This is what I got using Net Torque and ΣFy

 

[haruspex]

Στ=τT-2τf
Tr=2(μFn)r
T=2μ[(mg-T)/(1-μ)]
This is what I got using Net Torque and ΣFy

Are the two normal forces the same? It is important to use different symbols for variables with potentially different values.